Simplified Load Distribution Factor for Use in LRFD Design

Abstract

The S-over equation for the load distribution factor (LDF) was first introduced in the 1930s in the AASHTO Standard. Finite element (FE) studies, however, have shown it to be unsafe in some cases and too conservative in others. AASHTO LRFD 1994 introduced a new LDF equation as a result of the NCHRP 12-26 project. This equation is based on parametric studies and FE analyses. It is considered to be a good representation of bridge behavior. However, this equation involves a longitudinal stiffness parameter, which is not initially known in design. Thus, an iterative procedure is required to correctly determine the LDF value. This need for an iterative design procedure is perceived by practicing engineers as the major impediment to widespread acceptance of the AASHTO LRFD equation. In this study, a new simplified equation that is based on the AASHTO LRFD formula and does not require an iterative procedure is developed. A total of 43 steel girder bridges and 17 prestressed concrete girder bridges in the state of Indiana are selected and analyzed using a sophisticated FE model. The new simplified equation produces LDF values that are always conservative when compared to those obtained from the FE analyses and are generally greater than the LDF obtained using AASHTO LRFD specification. Therefore, the simplified equation provides a simple yet safe specification for LDF calculation. This study also investigates the effects of secondary elements and bridge deck cracking on the LDF of bridges. The AASHTO LRFD LDF equation was developed based on elastic FE analysis considering only primary members, i.e., the effects of secondary elements such as lateral bracing and parapets were not considered. Meanwhile, many bridges have been identified as having significant cracking in the concrete deck. Even though deck cracking is a well-known phenomenon, the significance of pre-existing cracks on the live load distribution has not yet been assessed in the literature. First, secondary elements such as diaphragms and parapet were modeled using the FE method, and the calculated load distribution factors were compared with the code-specified values. Second, the effects of typical deck cracking and crack types that have a major effect on load distribution were identified through a number of nonlinear FE analyses. It was found that the presence of secondary elements can result in a load distribution factor up to 40% lower than the AASHTO LRFD value. Longitudinal cracking was found to increase the load distribution factor; the resulting load distribution factor can be up to 17% higher than the LRFD value. Transverse cracking was found to not significantly influence the transverse distribution of moment. Finally, for one of the selected bridges, both concrete cracking and secondary elements are considered to investigate their combined effect on lateral load distribution. The increased LDF due to deck cracking is offset by the contributions from the secondary elements. The result is that the proposed simplified equation is conservative and is recommended for determination of LDF.